The Parisian club has now won the prestigious cup on 14 different occasions.
Paris Saint-Germain needed a dramatic leveler followed by a successful spot-kick decider to overcome their arch-rivals in Kuwait and secure a record-extending fourth consecutive French Super Cup victory.
The Champions League holders appeared to be coasting towards a straightforward triumph in the showdown featuring the Ligue 1 champions and the French Cup winners after the French winger found the scoring in the opening stages.
However, the southern French side struck twice late to seize a shock advantage. First, the English forward scored from the penalty spot, before the defender unfortunately directed the ball into his own net for an own goal.
In a breathtaking turn of fortune, Goncalo Ramos grabbed a vital leveler in the final seconds to force the match into a deciding shootout. The Parisian shot-stopper Chevalier then emerged as the hero, saving decisive kicks from Matt O'Riley and Hamed Traore.
From the spot, Goncalo Ramos, the midfielder, the full-back, and the young talent all scored successfully for Paris Saint-Germain to seal a convincing shootout win.
Now 14-time champions Paris Saint-Germain, who faced last season's Ligue 1 runners-up Olympique de Marseille after achieving a domestic double, have now won this trophy for the 12th time in the past thirteen years.